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The Stability of Matter in Quantum Mechanics, by Elliott H. Lieb, Robert Seiringer
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Research into the stability of matter has been one of the most successful chapters in mathematical physics, and is a prime example of how modern mathematics can be applied to problems in physics. A unique account of the subject, this book provides a complete, self-contained description of research on the stability of matter problem. It introduces the necessary quantum mechanics to mathematicians, and aspects of functional analysis to physicists. The topics covered include electrodynamics of classical and quantized fields, Lieb-Thirring and other inequalities in spectral theory, inequalities in electrostatics, stability of large Coulomb systems, gravitational stability of stars, basics of equilibrium statistical mechanics, and the existence of the thermodynamic limit. The book is an up-to-date account for researchers, and its pedagogical style makes it suitable for advanced undergraduate and graduate courses in mathematical physics.
- Sales Rank: #1357033 in Books
- Published on: 2009-12-14
- Original language: English
- Number of items: 1
- Dimensions: 9.72" h x .79" w x 6.85" l, 1.55 pounds
- Binding: Hardcover
- 310 pages
Review
Pre-publication praise: "This is an outstanding book which will be used both for research and for teaching. It will make an excellent text for a graduate course in either a physics or mathematics department. Physics students will learn to appreciate the beauty and relevance of mathematics and vice versa. The authors are leaders in the field. Their book not only describes important results but also makes them exciting."
Joel Lebowitz, Rutgers University
Pre-publication praise: "The stability of matter - in the sense that the binding energy of any agglomerate of particles never exceeds their rest energy - is one of the important contributions of quantum mechanics to the functioning of our cosmos. But quantum mechanics alone is not enough. It is necessary to distinguish the difference between the two kinds of elementary particles, fermions and bosons, for the tremendous increase of the binding energy with the number of bosonic particles violates the required energy bound and makes them unsuitable for ordinary matter. Maybe that's why we live in a fermionic world. These subtleties and much more are hidden in the innocent looking Schroedinger equation. To distill that out you need the appropriate mathematical tools, as provided in this magnificent book where on each page you can feel the hands of masters of the subject."
Walter Thirring, University of Vienna
Pre-publication praise: "Why does matter, from the size of atoms to stars avoid collapse? "The Stability of Matter in Quantum Mechanics" gives an impeccably written, self-contained introduction to the gems of this subject and the beautiful work of Elliott Lieb and coworkers over the past several decades. Every argument is ideally polished in this concise masterpiece. This book is an absolute must for any graduate students and active researchers, both mathematicians and physicists, interested in how a powerful yet elegant mathematics has answered one of the fundamental problems in mathematics and physics."
S-T Yau, Harvard University
"This book enjoys all the qualities that make it certain to become a standard reference for both researchers as well as students in the stability of matter field for many years to come."
H. Hogreve, Mathematical Reviews
"...the book's pedagogical style carefully guides them through the physical concepts and relevant mathematics before putting all the pieces together. Students and teachers alike will enjoy a marvelous experience as they learn from [this book]." Physics Today
About the Author
Elliott H. Lieb is a Professor of Mathematics and Higgins Professor of Physics at Princeton University. He has been a leader of research in mathematical physics for many decades, and his achievements have earned him numerous prizes and awards, including the Heineman Prize in Mathematical Physics of the American Physical Society, the Max-Planck medal of the German Physical Society, the Boltzmann medal of the International Union of Pure and Applied Physics, the Schock prize in mathematics by the Swedish Academy of Sciences, the Birkhoff prize in applied mathematics of the American Mathematical Society, the Austrian Medal of Honor for Science and Art, and the Poincaré prize of the International Association of Mathematical Physics.
Robert Seiringer is an Assistant Professor of Physics at Princeton University. His research is centred largely on the quantum-mechanical many-body problem, and has been recognized by a Fellowship of the Sloan Foundation, by a U.S. National Science Foundation Early Career award, and by the 2009 Poincaré prize of the International Association of Mathematical Physics.
Most helpful customer reviews
1 of 1 people found the following review helpful.
A masterpiece of mathematical Physics
By Maxim Kämmerer
This so-called review is ragged and from a professional perspective definitely meaningless. Quantum mechanics developed by Heisenberg and others is a theory generalizing classical mechanics and relativistic field theory to the atomic scale. The classical laws of physics do not apply there. They emerge on a larger scale as a limit case. To argue on the basics of not applicable physical laws is hardly a scientific approach. While Heisenberg uncertainty principle explains (not postulates) that atoms do not collaps, it does not explain why we are not a few millimeters tall. Freeman Dyson realized that it was a mathematically well posed and managable task to address this question with the mathematical tools of functional analysis. But it was Elliott Lieb alone or together with a hand full of coworkers who actually did the work in almost all relevant cases and provided these pioneering, ingenious, very accurate and last but not least rigorous results. The authors of this book did a great job in presenting the complicated matter in a coherent and comprehensable way, thereby making it accessable to students and non-specialists. The importance of the original works reviewed here can hardly be overestimated and it is a shame that the Nobel committee ignored them for so long, while awarding in part far less important achievements.
2 of 10 people found the following review helpful.
Quantum Mechanics does not explain the Stability of Matter
By Vic Dannon
The problem of the stability of matter was raised at the end of the nineteenth century:
To prevent the negatively charged electron from falling onto the positively charged nucleus, the electron was assumed to orbit the nucleus. Thus, the electric attraction between the electron and the proton would be balanced by the centripetal force of the central motion.
Since an orbiting electron is accelerating towards the center, the electron would radiate its energy, and spiral onto the nucleus. This raised again the question of the stability of matter. Namely, how does an Atom not collapse in a split second, as Electrodynamics shows that it should.
To answer that question, Bohr conjectured that the orbits of the electron around the nucleus are of fixed energy, and momentum. That the electron moved in loss-less energy orbits, so that no spiraling onto the nucleus may occur.
Bohr's conjecture did not explain how these lossless orbits were available: It seemed right to claim that the momentum was quantized in units of h-bar just like the radiation energy was quantized in units of h (h being the Planck constant). And the Conjecture lead to a credible explanation of the Hydrogen Spectrum.
Nevertheless, the question of the stability of matter was only reformulated: The electron does not spiral onto the nucleus because it stays in lossless orbits. But how are there lossless electron orbits? because Bohr conjectured so? Because the electron minds that its orbital momentum be quantized?
Note that the question of radiation in the orbit was raised by Classical Electrodynamics, and to avoid a contradiction between Electrodynamics and Quantum Mechanics, the answer should come from Electrodynamics.
In a recent paper, ([...]) we explained that in the lossless energy orbits, the radiation energy lost by the proton in its (very small) orbit around the center of the motion, compensates for the radiation energy lost by the electron in its orbit around the center of the motion.
First, Quantum Mechanics cannot be used to resolve an Electrodynamics problem, without leaving a contradiction between the two theories.
Second, the later Quantum Mechanics of Dirac, Heisenberg, and Schrödinger is based on its own postulates. By applying Quantum Mechanics to the problem of the Stability of matter, we are applying postulates that may very well guarantee the stability of matter. We then establish the stability of matter by assuming the stability of matter. A potential logical failure.
Third, the book is devoid of physical intuition, and counts on Abstract mathematical analysis, for which the reader is referred to the author's other book.
If you are seeking a credible explanation to the stability of matter, you will not find it in this book.
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